Some Recent Advances in the Numerical Solution of Differential Equations

机译：微分方程数值解的最新进展

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The purpose of the talk is the presentation of some recent advances in the numerical solution of differential equations, with special emphasis to reaction-diffusion problems, Hamiltonian problems and ordinary differential equations with discontinuous right-hand side. As a special case, in this short paper we focus on the solution of reaction-diffusion problems by means of special purpose numerical methods particularly adapted to the problem: indeed, following a problem oriented approach, we propose a modified method of lines based on the employ of finite differences shaped on the qualitative behavior of the solutions. Constructive issues and a brief analysis are presented, together with some numerical experiments showing the effectiveness of the approach and a comparison with existing solvers.

机译：谈判的目的是介绍微分方程数值解的一些最新进步，特别强调反应 - 扩散问题，哈密顿问题和具有不连续右侧的常微分方程。作为一个特殊情况，在本短文中，我们专注于通过特别适合该问题的特殊用途数值方法对反应扩散问题的解决方案：实际上，在面向问题的方法之后，我们提出了一种基于的改进的线条方法在解决方案的定性行为上采用有限差异。呈现建设性问题和简要分析，以及一些数值实验，显示了方法的有效性和与现有溶剂的比较。

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《International Conference of Numerical Analysis and Applied Mathematics》|2016年|various paging|共4页
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作者
Raffaele DAmbrosio;
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中图分类 TB9-53;
关键词
Numerical methods; partial differential equations; trigonometrical fitting;

机译：数值方法;部分微分方程;三角拟合;

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1. Discussion on ????????Numerical solution of 2nd-order hyperbolic partial differential equations by the method of continuous characteristics????????, ????????Analogue solution of 2nd-order hyperbolic partial differential equations by the method of continuous characteristics???????? and ????????Analogue solution of elliptic differential equations by conformal transformations???????? [J] . Electrical Engineers, Proceedings of the Institution of . 1971,第6期

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2. Numerical solution of Fuzzy Hybrid Differential Equation by Third order Runge Kutta Nystrom Method Numerical solution of Fuzzy Hybrid Differential Equation by Third order Runge Kutta Nystrom Method [J] . N. Saveetha, S.Chenthur Pandian Mathematical Theory and Modeling . 2012,第4期

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3. NUMERICAL SOLUTION OF BLACK – SCHOLES PARTIAL DIFFERENTIAL EQUATION USING DIRECT SOLUTION OF SECOND - ORDER ORDINARY DIFFERENTIAL EQUATION WITH TWO - STEP HYBRID BLOCK METHOD OF ORDER SEVEN [J] . H.K. Oduwole, J.K. Odeyemi, O.O. Olaiya Science World Journal . 2019,第2期

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4. Recent Advances in the Numerical Solution of Hamiltonian Partial Differential Equations [C] . Luigi Barletti, Luigi Brugnano, Gianluca Frasca Caccia, International Conference "Numerical Computations: Theory and Algorithms" . 2016

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8. Numerical Grid Generation. Proceedings of a Symposium on the Numerical Generation of Curvilinear Coordinate Systems and their Use in the Numerical Solution of Partial Differential Equations, held April 1982, Nashville, Tennessee. [R] . Thompson, J. F. 1982

机译：数值网格生成。 1982年4月，田纳西州纳什维尔举行的曲线坐标系数值生成及其在偏微分方程数值解中的应用研讨会论文集。

Some Recent Advances in the Numerical Solution of Differential Equations

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